High-precision eigenvalues of the neutron transport equation by the Carlvik method

High-precision results for solutions of neutron transport problems are important as a guidance to code developers and to understand the impact of physical and numerical approximations. The aim of this work is the determination of the eigenvalues of the transport equation in plane geometry, reaching results as accurate as one may desire, with practically no limitation in the number of exact digits required. The method proposed by Carlvik is re-visited and implemented through appropriate analytical manipulations within the Mathematica framework, exploiting some specific features of this software to keep a full control of the numerical precision throughout the whole calculation procedure. The Wynn-epsilon acceleration scheme is also used to improve the convergence trend. Some selected high-precision results are presented to illustrate the performance of the algorithm.